Communications utilizing frequency-hopping spread spectrum (FHSS), as shown in FIG. 1, have a number of advantages that include combating interference/jamming, operating with large near/far dynamic range typical of networked communication, and reducing transmit energy density. A common method of providing multiple access (MA) for FHSS systems is to allow nodes to transmit on different frequency hopping sequences (channels) simultaneously. For security considerations, it is ideal to make it appear that hop sequence selection is entirely random to observers that do not have access to side information (pseudorandom keystream) shared between the transmitter and intended receiver(s). Allowing two or more simultaneous transmissions to select hopping sequences at random results in collisions that can affect the reception of transmissions at the intended receivers. This is especially true in the case where the number of available hop frequencies is not very large relative to the number of channels required for the application. Even if hop sequences do not collide exactly, performance can still be impacted. For example, if at a particular hop period, a first hop sequence (channel) selects a frequency close to a frequency selected by a second hop sequence (channel), and the second sequence is received at a higher signal level by a receiver trying to receive the first sequence, then this receiver may not have the frequency selectivity required to receive the first sequence without degradation.
Previous approaches to frequency hopping access have included computing a frequency hopping sequence for a contiguous set of frequency bands based on a pseudorandom binary sequence generated by a shift register; adapting to a poor communication environment by switching the current frequency allocation to an alternate pre-defined allocation; generating a frequency hopping sequence based on random numbers generated by a linear feedback shift register (LFSR), a number of hop frequencies, and a minimum frequency separation between hops in a sequence; and generating a time varying partition of orthogonal frequency-division multiplexing (OFDM) subcarriers to users based on outputs of an Advanced Encryption Standard (AES)-seeded LFSR.
Many modern applications require flexibility with respect to the ratio of available hop frequencies to number of channels required, as available bandwidth and interference environments can severely impact the number of hop frequencies available. Thus, there is a need for generating secure frequency separation constrained hopping sequences for flexible frequency hopping access (FFHA) in an efficient manner.